December 17

1. A 72 ft. pipe is cut into two pieces of lengths in a 5:7 ratio. What are the lengths of the two pieces?

2. A shirt has been discounted 30% and is on sale for $36.00. What was the original price of the shirt?

3. Find a number so that 20 more than one-third of the number equals three-fourths of that number.

4. x + 2 + x - 1

3 2= 2 5. x + 3 = x - 2

6 4

6. What is the

Unit Price?

Linear Equations form straight lines. How do we determine if an equation is linear:

It can be rewritten in the form: Ax + By = C

This is the Standard Form of a linear equation where:

a.) A and B are not both zero.

b.) The largest exponent is not greater than 1

Determine Whether the Equations are Linear:

1. 4 - 2y = 6x 2. -4/5x = -2 3. -6y + x = 5y - 2

Remember:This is to determine whether an equation is linear (forms a straight line) or not. The standard form is also used to determine x and y intercepts.

Graphing Equations: y = mx

Graph the equation and tell whether it is linear.

y = –3x

4

The equation y = –

is a linear equation.

3x4

Graphing Equations: y = mx

1. (2,5) These numbers are called:

2. { (2,5); (3,7); (4,9) } This group of ordered pairs is a:3. A certain type of relation is a function. Describe a function.

Determining a Function:

4a.) If you have a relation of{ (2,5); (3,7); (4,9) }, then you can use _________ to determine function.

4b.) If the ordered pairs are graphed, then use this test:_________

3. Equation with only one dependent var. for each independent

5. The x values of a relation are known as the _______

6. The y values form the __________

7. Input values of a function come from the ________

8. Once the function is calculated, the output forms the ______

9. The dependent variable can also be written in:

_________ __________.

10. If the f(x) = 3/4x - 1/2, then solve for: f(3)

Test Review: Determining Solutions to Equations

11. Is the point (-1,-2) a solution to the equation y = 2x - 4

12. Find three points that are a solution to: 2x = y + 4

Intercepts

13. Name the x and y intercepts for lines A & B.

15. Find the x and y intercepts for: y = -3x + 6 and y - 2 = 4x

14. For each line, state whether it is positive, negative, or neither.

If you are solving an equation by using a table, then you want the equation to be in y = mx + c form. For example, if the equation is 2x + y = 4, you want to rewrite the equation as y = -2x + 4. You then plug in values for x, and solve for y

Ax + By = Cor

You can put the equation in Standard Form,find the intercepts, and use the slope to find other points

As you know, every point on a coordinate plane is the intersection of two variables, the independent x, and the dependent y.

What if, however, your equation only has an independent xvariable? 2x - 2 = -4

These equations can still be solved by finding the x intercept, since we know that at this point, y = 0

How is it Done?

Graph the equation: 2x - 2 = - 4

1. First, set the equation equal to zero: 2x + 2 = 02. Replace 0 with f(x)3. Make a table4. Graph the ordered pairs

Graph the function

Last Practice:

** Graph 5x + 2 = 7